Robust inference for geographic regression discontinuity designs: assessing the impact of police precincts

We study variation in policing outcomes attributable to differential policing practices in New York City (NYC) using geographic regression discontinuity designs. By focusing on small geographic windows near police precinct boundaries we can estimate local average treatment effects of precincts on arrest rates. The standard geographic regression discontinuity design relies on continuity assumptions of the potential outcome surface or a local randomization assumption within a window around the boundary. While these assumptions are often thought to be more realistic than other assumptions used to infer causality from observational data, they can easily be violated in realistic applications. We develop a novel and robust approach to testing whether there are differences in policing outcomes that are caused by differences in police precincts across NYC. In particular, our test is robust to violations of the assumptions traditionally made in geographic regression discontinuity designs and is valid under much weaker assumptions. We use a unique form of resampling to identify new geographic boundaries that are known to have no treatment effect, which provides a valid estimate of our estimator's null distribution even under violations of standard assumptions. We find that this procedure gives substantially different results in the analysis of NYC arrest rates than those that rely on standard assumptions, thereby providing more robust estimates of the nature of the effect of police precincts on arrest rates in NYC.